We present numerical experiments on gradient flows from [1]}.
Given a set of particles \(\theta = \lbrace (x_i, r_i)_i \rbrace \)  with coordinates \(x_i \in ^d\)  and masses \(r_i \in _+\) , one wishes to study their trajectories to minimize some potential \(\theta \mapsto F(\theta )\) .
The particles initialized at \(t=0\)  by \(\theta _0\)  undergo the dynamic \(\partial _t\theta (t) = - \nabla F(\theta (t))\) .
These dynamical systems are ubiquitous to model phenomena such as physical systems or crowd motions.
They also gained attention in machine learning to model the dynamics of neural networks training [2]}.
